Decadal cyclical geological atmospheric emissions for a major marine seep field, offshore Coal Oil Point, Southern California

The greenhouse gas, methane, budget has significant uncertainty for many sources, including natural geological emissions. A major uncertainty of geological methane emissions, including onshore and offshore hydrocarbon seepage from subsurface hydrocarbon reservoirs is the gas emissions’ temporal variability. Current atmospheric methane budget models assume seepage is constant; nevertheless, available data and seepage conceptual models suggest gas seepage can vary considerably on timescales from second to century. The assumption of steady-seepage is used because long-term datasets to characterize these variabilities are lacking. A 30-year air quality dataset downwind of the Coal Oil Point seep field, offshore California found methane, CH4, concentrations downwind of the seep field increased from a 1995 minimum to a 2008 peak, decreasing exponentially afterward with a 10.2-year timescale (R2 = 0.91). Atmospheric emissions, EA, were derived by a time-resolved Gaussian plume inversion model of the concentration anomaly using observed winds and gridded sonar source location maps. EA increased from 27,200 to 161,000 m3 day−1 (corresponding to 6.5–38 Gg CH4 year−1 for 91% CH4 content) for 1995–2009, respectively, with 15% uncertainty, then decreased exponentially from 2009 to 2015 before rising above the trend. 2015 corresponded to the cessation of oil and gas production, which affects the western seep field. EA varied sinusoidally with a 26.3-year period (R2 = 0.89) that largely tracked the Pacific Decadal Oscillation (PDO), which is driven on these timescales by an 18.6-year earth-tidal cycle (27.9-year beat). A similar controlling factor may underlie both, specifically varying compressional stresses on migration pathways. This also suggests the seep atmospheric budget may exhibit multi-decadal trends.


S.2. West Campus Station Time Series Data
Significant variations on daily to seasonal to interannual time scales are apparent in the WCS time series (Fig. S1). Concentrations and emissions hereafter are for total hydrocarbon, THC. WCS data quality improved significantly in 2008, with measurements decreasing from 1-hour to 1-minute time resolution and an extended measurement range that allowed higher values of C and u to be recorded.

S.3. Seep Trends
( , !""# ) for WCS decreased slowly from 1990 to 1995 and then generally increased through 2008 (with short maxima and minima in 2003 and 2005), followed by a decline through 2017 (Figs.  4, S4). The seasonal trend was best fit by a least-squares linear regression by a two-part 365.3-day period (124-ppb amplitude) sine function with a peak in winter. The discrete fit accounted for a small phase offset around 2008. The sinusoidal function was subtracted from the 2008-2020 data and then fit with an exponential function by a least-squares linear-regression analysis (Fig. S2). The seasonal trend likely relates partly to wind speed (which induces waves), particularly associated with storms.

S.4. California and Northern Hemisphere Methane Trends
The overall WCS ( , seep ) trend differs dramatically from the California CH4 trend, represented by the Walnut Grove tall tower, and the CH4 trend for the Northern Hemisphere, represented by Mauna Loa, Hawaii (Fig. S3). Hourly CH4 concentrations for the Walnut Grove tall tower (inlet at 423 m) were rolling-median filtered (75 hours) to remove short excursion from local sources, leaving a seasonal cycle superimposed on interannual growth. The interannual trend was fit with a 2 nd -order polynomial (R 2 =0.73) with an average increase of 7.28 ppb yr -1 . A single sinusoid was well fit to the detrended residual with a 1-yr cycle, peaked in winter, which found an amplitude of 20.2 ppb (R 2 =0.8). The winter peak large arises from the lower planetary boundary layer as many emission sources are at a minimum in winter. The California cycle runs counter to the seasonality of most emission sources (microbial from wetlands and agricultural emissions are temperature sensitive and thus higher in the summer) and results from a shallower winter boundary layer than in the summer (Mark Fischer, personal communication, 2020). Seasonal changes in hydroxyl concentration and resultant CH4 loss also play a role.
Mauna Loa, Hawaii CH4 data showed rapid growth in the late 1980s, stabilizing from ~2000 to 2008, before growing approximately linearly at 7.54 ppb yr -1 . The seasonal cycle in the Mauna Loa data was 11 ppb from a sinusoidal fit to the residual of a 3 rd -order polynomial fit. Mauna Loa seasonality is much less than the seep field background seasonality.
In part, this is due to the higher altitude of Mauna Loa (and Walnut Creek); however, Trinidad Head is at sea level and also exhibits a much smaller seasonal cycle than the seep field. Notably, the Seep Field background trend is very different from the NOAA station trends and is at much higher concentrations. This difference demonstrates the importance of local seep field emissions in the Santa Barbara basin, where recirculation of CH4-laden waters occurs due to gyre-like currents  and air that can recirculate as part of the sea-breeze cycle (Dorman and Winant, 2000). Additionally, the largest or second largest in terms of oil emissions seep field in California, is situated to the west of the COP seep field (prevailing upwind), the extensive Concepcion Seep Field, where gas seep bubbles have been documented . Currently, no emissions assessments are available. This strongly suggests that seepage has a significant impact on Santa Barbara Channel CH4, with contributions from other regional sources.

S.5. Direction Resolved Seep Trends
Prevailing winds are strongest from the west due to topographic forcing from the coastal mountain range -in this direction, concentrations are the lowest, which is consistent with no mapped seepage in that direction (Fig. S4).

S.6. Modeled Emissions
The Cycle simulation (Fig. S5) was well fit by an offset sinusoidal function with amplitude (94,000 m 3 day −1 ), and a 26.3-year period around a cycle average of 90,300 m 3 day −1 ). The exponential decrease for the Annual simulation (Fig. 8A) had a 10.2-year time scale; however, the seasonal simulation (Fig. S6) found a shorter time scale -9.6 years.  Individual time-window simulation maps (Figs. S7-S8) show the same overall trends as C' (Fig.  4), with an EA minimum in 1995 and a peak around 2009-2010. Using the higher quality data since 2008, 1-year simulations showed a peak EA of 156,000 m 3 day -1 . This was approximately six times the minimum of 27,200 m 3 day -1 .

S.7. Methodological Differences
The primary difference between a sonar survey seep field emission estimate and an air quality station emissions estimate is that the latter is continuous, including the stormy season when sonar surveys cannot be safely conducted. In contrast, sonar surveys only provide a snapshot of a phenomenon that is highly variable, see review in . The simulations show a clear seasonal trend (Fig. S6), with a summer minimum when sonar surveys are preferentially scheduled due to calmer winds ( Fig. 2A) and lower waves. Also, during summer, large transient emissions are at a minimum. Seasonality was not addressed by either sonar survey. In contrast, WCS data are continuous.
Other sources of variability include tidal variations (Boles et al., 2001), diurnal wind cycles (Leifer et al., 2021), and transient seepage eruptions, which are challenging to address in a sonar survey. Furthermore, sonar surveys are spatially limited, although emissions can (and do) occur from areas outside the survey area -areas that may be active in other seasons. In this regard, Padilla et al. (2019) significantly under-surveyed the seep field (4.1 of 18 km 2 ).
By contrast, the plume inversion approach captures emissions, including variations and transient emissions and emissions from outside the surveyed area of the seep field. As such, the near